Lutasin ang 12/sqrt{1-frac{100{910^16}}}

$$\frac{ 12 }{ \sqrt{ 1- \frac{ 100 }{ 9 { 10 }^{ 16 } } } }$$

I-evaluate

$$\frac{360000000\sqrt{899999999999999}}{899999999999999}\approx 12$$

Mga Hakbang ng Solution

Kalkulahin ang 10 sa power ng 16 at kunin ang 10000000000000000.

$$\frac{12}{\sqrt{1-\frac{100}{9\times 10000000000000000}}}$$

I-multiply ang 9 at 10000000000000000 para makuha ang 90000000000000000.

$$\frac{12}{\sqrt{1-\frac{100}{90000000000000000}}}$$

Bawasan ang fraction \frac{100}{90000000000000000} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 100.

$$\frac{12}{\sqrt{1-\frac{1}{900000000000000}}}$$

I-convert ang 1 sa fraction na \frac{900000000000000}{900000000000000}.

$$\frac{12}{\sqrt{\frac{900000000000000}{900000000000000}-\frac{1}{900000000000000}}}$$

Dahil may parehong denominator ang \frac{900000000000000}{900000000000000} at \frac{1}{900000000000000}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.

$$\frac{12}{\sqrt{\frac{900000000000000-1}{900000000000000}}}$$

I-subtract ang 1 mula sa 900000000000000 para makuha ang 899999999999999.

$$\frac{12}{\sqrt{\frac{899999999999999}{900000000000000}}}$$

I-rewrite ang square root ng division na \sqrt{\frac{899999999999999}{900000000000000}} bilang division ng mga square root na \frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}.

$$\frac{12}{\frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}}$$

Kalkulahin ang square root ng 900000000000000 at makuha ang 30000000.

$$\frac{12}{\frac{\sqrt{899999999999999}}{30000000}}$$

I-divide ang 12 gamit ang \frac{\sqrt{899999999999999}}{30000000} sa pamamagitan ng pagmu-multiply sa 12 gamit ang reciprocal ng \frac{\sqrt{899999999999999}}{30000000}.

$$\frac{12\times 30000000}{\sqrt{899999999999999}}$$

I-rationalize ang denominator ng \frac{12\times 30000000}{\sqrt{899999999999999}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{899999999999999}.

$$\frac{12\times 30000000\sqrt{899999999999999}}{\left(\sqrt{899999999999999}\right)^{2}}$$

Ang square ng \sqrt{899999999999999} ay 899999999999999.

$$\frac{12\times 30000000\sqrt{899999999999999}}{899999999999999}$$

I-multiply ang 12 at 30000000 para makuha ang 360000000.

$$\frac{360000000\sqrt{899999999999999}}{899999999999999}$$